Yes, it is but it might not mean what you think it means. Compare the difference between "make a test" and "do a test" - the teacher might make a test for the student to do.

It's correct, but I think the word "try" fits better: "I will try another experiment."

Technically yes though I normally hear people use either the verb "to do" or "to perform" in this scenario. "I will do another experiment" "I will perform another experiment" Hope this helps :)

no... must be "run" or "carry"